R. D. Berlin Center for Cell Analysis & Modeling, U. Connecticut School of Medicine, Farmington, CT, United States of America.

2

Department of Pharmacological Sciences, and Division of Nephrology, Icahn School of Medicine at Mount Sinai, New York, NY, United States of America.

3

Department of Mechanical Engineering, Columbia University, New York, NY, United States of America.

4

National Center for Microscopy and Imaging Research, UCSD, San Diego, CA, United States of America.

Abstract

Kidney podocytes' function depends on fingerlike projections (foot processes) that interdigitate with those from neighboring cells to form the glomerular filtration barrier. The integrity of the barrier depends on spatial control of dynamics of actin cytoskeleton in the foot processes. We determined how imbalances in regulation of actin cytoskeletal dynamics could result in pathological morphology. We obtained 3-D electron microscopy images of podocytes and used quantitative features to build dynamical models to investigate how regulation of actin dynamics within foot processes controls local morphology. We find that imbalances in regulation of actin bundling lead to chaotic spatial patterns that could impair the foot process morphology. Simulation results are consistent with experimental observations for cytoskeletal reconfiguration through dysregulated RhoA or Rac1, and they predict compensatory mechanisms for biochemical stability. We conclude that podocyte morphology, optimized for filtration, is intrinsically fragile, whereby local transient biochemical imbalances may lead to permanent morphological changes associated with pathophysiology.

(A) In order to reconstruct the complete podocyte volume including all the foot processes, we manually segmented stacks of SBEM images. This was done by reviewing the entire stack and identifying all of the projections that emanate from the cell body. (B) At full resolution, geometric details of individual foot processes can be seen. (C) We then thresholded the segmented images to obtain continuous binary stacks that can be extruded in Rhinoceros and combined in Virtual Cell to form (D) a reconstructed 3-D volume. (E) We quantified the volume and surface area share of foot processes (FPs) by imposing a Gaussian surface filter in Seg3D, which removed all surface projections smaller than 440 nm. (F) We used a commonly used heat transfer model to identify the cell body of the cells: a cytoplasmic specie was uniformly synthesized and allowed to diffuse into the membrane until steady state. Regions with low surface area-to-volume ratios, i.e., cell body, maintain ~90% of the maximum value. (G) These sections were assigned as the cell body. (H) From the reconstructed volumes, length and angles for major processes and branches were measured using Imaris; the lime colored rendered volume represents the cell volume whereas colored internal lines are the measured paths for the branches. (I) For clarity, the internal lines are shown without the rendered volume. Sample branching patterns for two of the cells are shown in supplementary . (J) Using the volume, surface area, and branching information, a representative geometry is constructed. For computational simplicity, we assumed symmetry about the xy- and yz-planes, and hereby only half of these are shown. Rat podocytes (RP) used in this figure are RP1, RP8, RP9, RP11, and RP13, respectively, and morphological characteristics of these cells are shown in .

(A) Reaction diagram and nomenclature for parameters. Each parameter represents the rate of conversion between the two species marked by the arrows. (B) Summary for relationship between nullclines and parameters αf, βf, αb and βb. Blue curves are nullclines for and red curves for . The arrows represent the direction of change of a given nullcline when the shown parameter increases. The gray shaded region represents the “effacement region” where actin in FPs does not form adequate amount of bundles and maintain a stable FP morphology. (C) A system with strong positive feedback (αf, or weak dissociation rate, βf) has a single stable equilibrium point. The concentrations for bundles and F-actin in the dashed trajectory of the phase plane (left, dashed gray line) are plotted in the time-series to the right, in red and blue, respectively. (D) Weak positive feedback (αf) or strong dissociation rate (βf) give rise to a second stable equilibrium point, representing the collapse of bundles. The concentrations for the solid trajectory in the phase plane (left) are plotted with the solid lines in the time series (right). (E) Weak bundle turnover rate (βb) or strong bundling (αb) destabilizes the system, and there are no longer stable equilibrium points. However, the cyclic behavior might be able to keep the bundles sufficiently strong at all times. (F) A combination of weak bundle turnover rate (βb or strong bundling, αb) and weak positive feedback (αf) results in complete collapse of the actin cytoskeleton. Model parameters listed in . All concentrations are non-dimensional.

Analysis of bundle stability in the face of spatial differences in positive feedback (αf), using an ODE model composed of 2 FP compartments.

One FP fractional compartment (FP2) is subject to a stimulus that increases actin polymerization by Δαf, whereas the remaining fraction (FP1) is subject to nominal polymerization conditions, αf. This stimulus may either be sustained (shown in A) or transient (shown in B-G). (A) A 3-D plot showing steady state bundles on the vertical axis as a function of Δαf/αf and FP2 (log scale). For this sustained enhancement, the bundle intensity in FP1 (blue mesh) and FP2 (red mesh) depend on the intensity Δαf and the relative proportions of FP2 to FP1 (FP1 + FP2 = 1). As Δαf increases, FPs with stronger feedback form stronger bundles. If the fraction of FPs with enhanced feedback (FP2, red mesh) is small, the FPs with normal αf (FP1, blue mesh) are unperturbed, while the bundles in FP2 are strengthened. Because there is a fixed total amount of actin, stronger bundling in FP2 drains actin available for bundles in FP1 until a threshold is reached at which collapse of actin bundles in FP1 is observed. (B) Time course of a transient stimulus applied at t = 40. In C-E, the value of Δαf follows this time course, with varying intensities; equal volume fractions for FP1 and FP2 were used, with red curves corresponding to FP2 and blue to FP1. (C) A small perturbation allows the system to return to the pre-stimulus steady state. (D) When the maximum Δαf/αf = 1 (i.e. FP2 transiently reaches twice that of FP1), a new stable steady state is generated where bundles have collapsed in FP1 and increased in FP2. (E) When the maximum Δαf/αf = 2 (i.e. FP2 transiently reaches 3 times that of FP1) there is a transient increase in FP2 bundles followed by collapse and enhanced bundles in FP1. The behavior displayed in C, D and E is the hallmark of a tristable system. See the text for an explanation. (F). The steady state values for concentration of bundles in fractions FP1 (blue) and FP2 (red) are shown as a function of stimulus intensity, consistent with C-E. (G) Different fractions of FP1 and FP2 will impact the steady state values (see also ).

(A) Diagram of a region of a podocyte at steady state. A transient jump in αf, as in , was locally applied to the region labeled FP2 and the state of actin throughout the podocyte was simulated over time. The inset shows bundle concentrations over time in four FPs, two within the FP2 segment and two outside it, identified by colored arrowheads and lines. (B) Zoomed snapshot of the highlighted region is at time = 200 and (C) time = 1000.

A-C. Progressive loss of FPs due to a continued decrease of βb imposed at time t = 0; snapshots at time (A) t = 0, (B) t = 500, and (C) t = 1500. D-J. Tests of combinations of transient perturbation in βb and αf to explore compensatory mechanisms. (D) Return to baseline βb at time t1 = 500 results in (E) recovery of the majority of the remaining foot process bundle concentrations at t2 = 1500. (F) Decrease of αb at time t1 while holding βb constant results in (G) similar stabilization. Finally, (I) increase of αf while holding βb constant (J) produces similar spatial results. All three interventions prevent progressive effacement (compare C with E, G and J). (H) Timecourses for spatial average of bundle concentration in the FPs identified by arrows in snapshots E, G and J (at time 1500, gray arrowhead). Linestyle follows the same pattern as arrows. The same color scale is used for all the 3-D snapshots of bundle concentrations. Parametric perturbations are listed in .